Two-Photon Cooperative Absorption in Colliding Cold Na Atoms

Two-photon cooperative absorption is common in solid-state physics. In a sample of trapped cold atoms, this effect may open up new possibilities for the study of nonlinear effects. The experiment described herein starts with two colliding Na atoms in the $S$ hyperfine ground state. The pair absorb two photons, resulting in both a $P_{1/2}$ and a $P_{3/2}$ atom. This excitation is observed by ionization using an external light source. A simple model that considers only dipole-dipole interactions between the atoms allows us to understand the basic features observed in the experimental results. Both the pair of generated atoms and the photons originating from their decay are correlated and may have interesting applications that remain to be explored.

Figure 1

Diagrammatic representation of the levels and transitions of interest. (a) One-photon transitions in each atom from the ground state to one of the excited states ($3S_{1/2}\to 3P_{1/2}$ and $3S_{1/2}\to 3P_{3/2}$). (b) Two-photon cooperative absorption in both atoms from the ground state to the double excited state $(3S_{1/2}+3S_{1/2}\to 3P_{1/2}+3P_{3/2})$. (c) Representation of the probability of absorption ($PA$) as a function of probe frequency ($\omega$); when $\omega$ is equal to $\frac{{\omega }_{P_{1/2}}+{\omega }_{P_{3/2}}}{2}$, the presence of atomic interactions makes the transition to the excited states possible.

Figure 2

Schematic representation of the experimental system, where SA denotes saturated absorption; TP, turbo pump; IP, ion pump; Wm, wave meter; IL, ionization laser; EOM, electro-optical modulator; SB, slower beam; PB, probe beam; OF, optical fiber; and TB, trapping beam.

Figure 3

The time sequence is divided into two counting windows, $A$ and $B$. The first counts the ions formed by the ionization of the atoms in the excited states with energies equal to or higher than the $3P_{1/2}$ state due to absorption of the trap frequencies, i.e., the background ion counts. The second window counts the ions formed due to the absorption of the probe laser and the trap frequencies. The trap frequencies remain on during the whole measurement. The ion counts start 1 ms after the slower beam is shut down. The probe frequency is on during the counts in the second measurement window and off in the background counts.

Figure 4

Ion counts as a function of the probe frequency. From left to right, the first (last) peak is due to the ionization of the atoms excited to the $3P_{1/2}$ ($3P_{3/2}$) state. These peaks have shoulders that are due to hyperfine transitions. The central peak, shown in more detail in the small graph in the center, is evidence of the two-photon cooperative absorption.

Figure 5

Ion counts as a function of the probe intensity. A quadratic fit was plotted to see the expected behavior of two-photon cooperative absorption.

Figure 6

Ion counts as a function of the probe laser frequency in the region around the halfway point between the $3P_{1/2}$ and the $3P_{3/2}$ transitions (central peak of Fig. 4). The experimental data are compared with the theoretical curve expected from Eq. (1) (dotted line) and with Eq. (2) (continuous line), which takes into account the $R^{-3}$ dependence of the excited potentials. This finding demonstrates that the peak asymmetry comes from the $R^{-3}$ dependence of the potentials.